Laminar diffusion flamelets

For fast equilibrium chemistry (Section 5.4), an equilibrium assumption allowed us to write the concentration of all chemical species in terms of the mixture-fraction vector c(x, t) = ceq( (x, t)). For a turbulent flow, it is important to note that the local micromixing rate (i.e., the instantaneous scalar dissipation rate) is a random variable. Thus, while the chemistry may be fast relative to the mean micromixing rate, at some points in a turbulent flow the instantaneous micromixing rate may be fast compared with the chemistry. This is made all the more important by the fact that fast reactions often take place in thin reaction-diffusion zones whose size may be smaller than the Kolmogorov scale. Hence, the local strain rate (micromixing rate) seen by the reaction surface may be as high as the local Kolmogorov-scale strain rate. 

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Figure 5.17. A laminar diffusion flamelet occurs between two regions of unmixed fluid. On one side, the mixture fraction is unity, and on the other side it is null. If the reaction rate is localized near the stoichiometric value of the mixture fraction st, then the reaction will be confined to a thin reaction zone that is small compared with the Kolmogorov length scale.

Peters, N. (1984). Laminar diffusion flamelet models in non-premixed turbulent combustion. Progress in Energy and Combustion Science 10, 319-339. 

N. Peters. Laminar diffusion flamelet models in nonpremixed turbulent combustion. Prog. Energy Combust. Sci., 10 319-339, 1984. 

The method is based on a particular picture of the turbulent reacting flows it is assumed that it consist in a collection of reaction diffusion layers, which are continuously displaced and stretched within the turbulent medium. For the sake of simplicity, the layers are often assumed to be one dimensional, that is almost planar, with a thickness very small with respect to their main curvature radii, and similar to study laminar diffusion reaction layers. It is consequently possible to study separately these layers, or "reacting laminae", or "flamelets", and to compute their internal structure with all chemical details, like in a laminar flow. After that, it is necessary to build the turbulent field by a convenient collection of such a "lamina". 

The relevance of premixed edge flames to turbulent premixed flames can also be understood in parallel to the nonpremixed cases. In the laminar flamelet regime, turbulent premixed flames can be viewed as an ensemble of premixed flamelets, in which the premixed edge flames can have quenching holes by local high strain-rate or preferential diffusion, corresponding to the broken sheet regime [58]. 

At present, there exists no completely general RANS model for differential diffusion. Note, however, that because it solves (4.37) directly, the linear-eddy model discussed in Section 4.3 can describe differential diffusion (Kerstein 1990 Kerstein et al. 1995). Likewise, the laminar flamelet model discussed in Section 5.7 can be applied to describe differential diffusion in flames (Pitsch and Peters 1998). Here, in order to understand the underlying physics, we will restrict our attention to a multi-variate version of the SR model for inert scalars (Fox 1999). 

FlameMaster v3.3 A C+ + Computer Program for OD Combustion and ID Laminar Flame Calculations. FlameMaster was developed by H. Pitsch. The code includes homogeneous reactor or plug flow reactors, steady counter-flow diffusion flames with potential flow or plug flow boundary conditions, freely propagating premixed flames, and the steady and unsteady flamelet equations. More information can be obtained from http //www.stanford.edu/group/pitsch/Downloads.htm. 

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